Investigation on gas–solid flow regimes in a novel multistage fluidized bed

Gongpeng Wu,Yan He*

College of Electromechanical Engineering,Qingdao University of Science and Technology,Qingdao 266061,China

Keywords: Multistage riser Pressure fluctuation Flow regime Fuzzy C-means clustering Hilbert–Huang

ABSTRACT Gas–solid flow regime in a novel multistage circulating fluidized bed is investigated in this study.Pressure fluctuations are first sampled from gas–solid flow systems and then are analyzed through frequency and time–frequency domain methods including power spectrum and Hilbert–Huang transform.According to the flow characteristics obtained from pressure fluctuations,it is found that the gas–solid motions in the multistage circulating fluidized bed exhibit two dominant motion peaks in low and high frequencies.Moreover,gas-cluster motions become intensive for the multistage circulating fluidized bed in comparison with the fast bed.Unlike the traditional methods,the fuzzy C-means clustering method is introduced to objectively identify flow regime in the multistage circulating fluidized bed on the basis of the flow characteristics extracted from bubbling,turbulent,fast,and multistage fluidized beds.The identification accuracy of fuzzy C-means clustering method is first verified.The identification results show that the flow regime in the multistage circulating fluidized bed is in the scope of fast flow regime under examined conditions.Moreover,the results indicate that the consistency of flow regime between two enlarged sections exists.In addition,the transition onset of fast flow regime in the multistage circulating fluidized bed is higher than that in the fast bed.

1.Introduction

In the chemical industry,gas–solid fluidized bed reactors are widely used due to good reaction performance.Nevertheless,the uniformity of solid distribution in the fluidized bed largely affects gas–solid mixing and contact [1].A representative case is the occurrence of core-annulus flow structure in the riser.The solid distribution that dilute phase and dense phase occur in the core and annulus region respectively leads to low reaction efficiency.The multistage bed with enlarged sections gradually attracted attentions from researchers to improve the flow structure in fluidized beds [2–4].For this reason,a novel multistage fluidized bed was developed and applied to flue gas desulfurization[5].Previous investigators have made an effort on hydrodynamics in multistage beds.They found that gas–solid flow behavior changed and presented some distinctive flow characterizations [4–6].Although some reports showed that the circulating-turbulent regime existed in a circulating fluidized bed (CFB) riser with an enlarged section[7,8],many factors including bed structure,operating condition,and material affect flow regime in the multiphase system.Whether a circulating-turbulent flow regime emerges in the novel multistage bed still remains unclear.Moreover,flow regime is correlated to the design,scale-up,and operation of fluidized beds.Each flow regime exhibits individual hydrodynamic characteristics as well as heat and mass transfer levels,thereby resulting in different reaction properties.Therefore,gas–solid flow-regime needs to be investigated for the application of the multistage fluidized bed to desulfurization.

Previous flow regime identification is generally achieved by characterizing solid phase profiles such as particle concentration and velocity in fluidized columns.Qiet al.[9]identified the formation of circulating-turbulent flow regime in a novel fluidized bed with the enlarged section at the topviainvestigating macro-and micro-flow behavior.Issangyaet al.[10] found the generation of dense suspension flow after observing flow condition visually and analyzing solid holdup distributions.Evidently,this method hardly avoids subjectivity.Different approaches were proposed to provide objective identification of flow regime.Fuzzy C-means(FCM) clustering,a popular pattern recognition method,has been applied to flow regime determination in gas–liquid system[11,12]and gas–solid spouted bed[13].FCM clustering is an unsupervised clustering method.Compared with other pattern recognition methods such as artificial neural network and neuro-fuzzy interface system,the FCM method has less empirical input parameters and no sample training process.The FCM method has some advantages over other clustering techniques.For instance,a few user-defined parameters can improve the objectivity and accuracy of the identification result.Moreover,it is relatively insensitive to initializations and has minimum computational complexity.Although the FCM method exhibits good performance in flow regime identification [14,15],in the scope of the authors’ knowledge,this method has not been used to identify flow regime in the CFBs.Therefore,the FCM method was selected to perform flow regime identification in the novel multistage fluidized bed.

Various measurement techniques have been developed and applied to characterize flow regime.Common methods are easily found from reports,as follows [16–20]:image recording using high-speed camera,pressure fluctuation sampling by means of pressure transducers,void fraction acquisition employing electrical capacitance tomography or optical fiber probe,ray measurement with the help of radioactive source,and passive detection adopting acoustic emission.Among these measurement methods,pressure measurement is an easy,reliable,and noninvasive method,which is frequently selected to study flow regime in fluidized beds.On the other hand,pressure fluctuations contain dynamic characterizations of gas–solid flow.Consequently,selecting suitable analysis method is significant to obtain useful information from pressure fluctuations.Pressure signal can be analyzed using the following methods [21–23]:statistical analysis (time domain),spectrum analysis (frequency domain),Hilbert–Huang transform (HHT;time–frequency domain).Statistical analysis is simple and useful in processing pressure signal.Several statistical parameters such as auto-correlation function and standard deviation are often used.Spectrum analysis performed by discrete Fourier transform (DFT)generally concerns power spectrum density (PSD).HHT is a multi-resolution analysis method with time-adaptive decomposition.Liet al.[22]reported that the HHT method offered high resolution in identifying flow regimes.

The primary objective of this study is to study flow pattern in the multistage fluidized bed.First,flow characterizations extracted from bubbling,turbulent,fast,and multistage beds were compared and analyzed.Then the flow regime in the multistage fluidized bed was identified using the FCM method.Based on the identification results,the transition boundary of flow regime in the multistage bed was also investigated.

2.Experiments

To cover typical flow regimes in a gas–solid flow system,two experimental apparatuses are adopted.Fig.1(a) and (b) show the schematic diagram of nonrecycling fluidized bed and CFB,respectively.Nonrecycling bed is used to investigate the bubbling flow regime.The CFB includes two aspects,as follows:one is to study turbulent and fast flow regimes in the conventional CFB and flow regime in the multistage CFB;second is to obtain the transition boundary between turbulent and fast flow regimes in the multistage CFB.

Nonrecycling bed consists of wind chamber,fluidized bed column,and solid diffuser.The inner diameter and height of the column are 0.08 and 1.2 m,respectively.The wind chamber,together with a porous distributor,is 0.16 m tall to provide a relatively uniform gas distribution.The distributor plate is covered with a fine mesh net to avoid the leakage of solid particles in the main bed.The diffuser with an inner diameter of 0.24 m at the top of the main bed can relieve an escape of solid particles.Initially,solid particles are set at a certain static height in the bed.The fluidized air,supplied by a blower,is introduced into the gas chamber.The air flow rate is controlled via rotameters with different measuring ranges.A cyclone is used to intercept entrained particles.

As shown in Fig.1(b),the circulating system is composed of riser,cyclone,storage vessel,and return lag.The multistage riser consists of two enlarged sections with the same geometric structures and three straight sections.The riser height is 3.81 m and the height of each part is shown in Fig.1(b).The diameters of the enlarged section and straight section are 0.24 and 0.14 m,respectively.The conventional riser has a diameter of 0.14 m.A porous distributor is used to ensure a uniform air distribution.A stream of gas is introduced to the inclined pipe via a bypass to fluidize solids.Gas–solid mixtures move upwards and flow out of the riser.Solids separated from gas phase in the three-stage cyclone fall back into the storage vessel and then return to the riser through an inclined pipe.The solid circulation flux is regulated by a butterfly valve.The riser column is detachable,ensuring that the fluidization experiments are conducted in the conventional and multistage risers.The enlarged sections of the multistage bed can be replaced by the straight sections with the same length.

Pressure fluctuations generally reflect the dynamic behavior of gas–solid flow system.Thus,the identification of various flow regimes can be achievedviacharacteristic parameters extracted from pressure fluctuations.Compared with the differential pressure pulsation representing local dynamics,the absolute pressure signals reveal global dynamics in the fluidized bed.Therefore,absolute pressure fluctuations are measured to characterize flow regime.Pressure transducers with a full-scale accuracy of ±0.25% and two ranges of 0–2 and 0–10 kPa are used.Pressure signals sampled from transducers are transferred to a computer through an A/D converter and then recorded by Labview software.For each operating condition,we use the sampling frequency of 400 Hz for an interval of 90 s.A steel tube with a 0.005 m inner diameter and 0.06 m length is installed on the side of the wall.To prevent particles from entering into the transducer,a fine screen is placed at the tip of the steel probe.Pressure transducer and steel tube are connected by a polyurethane tube with 0.13 m length.Thus,the pressure distortion caused by the connector tube is negligible in this study[24].Pressure port is set at 0.11 m above the distributor in the nonrecycling bed.The heights of the sampling point are 1.45(the lower enlarged section)and 2.66 m(the upper enlarged section)in the multistage riser.The wavelet threshold method is first applied to eliminate high-frequency noises before analyzing the pressure data.

Considering that the multistage CFB (Fig.1(b)) is designed for the dry desulfurization process,the activated semi-coke serving as the sorbent in the process is used in this work.Different from the traditional Ca-based sorbent,the activated semi-coke is a carbon-based material produced from the coal.The activated semi-coke is used as solid phase in this work.For the nonrecycling bed,experiments are performed with the inlet velocity varying from 0 to 0.65 m?s-1.The static bed height is 0.16 m.In the CFBs,superficial gas velocity and solid circulation flux range from 1.2 to 3.5 m?s-1and from 0.25 to 3.25 kg?m-2?s-1,respectively.All experiments are conducted at room environment.

3.Methods

Flow characteristics of different flow regimes should be extracted from the pressure fluctuations before identifying the flow pattern in the multistage bed.We used spectrum analysis and HHT transform to distinguish flow regimes.

3.1.Power spectrum

Fig.1.Diagram of the experimental setup:(a) nonrecycling fluidized bed,(b) CFB.

Spectrum analysis is commonly used to reveal frequency domain characteristic of pressure signal,which can be performed by DFT.The DFT of a signal series is expressed by Eq.(1).Power spectrum density (PSD) is further obtained from the DFT.Specifically,time series is first divided into several segments.Then the window function is used to suppress the leakage of frequency spectrum for each segment.

3.2.HHT

HHT is an effective method for processing nonlinear and nonstationary signal,as a multi-resolution analysis method.It consists of empirical model decomposition (EMD) and Hilbert spectrum analysis [25].Pressure signal is first decomposed into a set of intrinsic mode functions (IMFs).Then,each IMF component is solved by the Hilbert transform.Through these steps,the local time–frequency features of signal are presented.Each IMF needs to satisfy two conditions,as follows:the number of extreme and zero-crossing points should be equal or differ at most by one in the entire signal series;the average of the two envelopes defined by the local maxima and minima is zero at any point.The reconstructed signal can be expressedviaEq.(2),as follows:

The Hilbert transform(Eq.(3))is applied to each IMF for obtaining instantaneous frequency.

Corresponding analytic signal is obtained as follows:

where the instantaneous amplitude and phase are computed as follows:

The instantaneous frequency is then calculated as follows:

Furthermore,the Hilbert spectrum is described as follows:

Moreover,the energy of each IMF can be defined as follows:

3.3.FCM

FCM is a useful clustering algorithm,which can classify a data set into different groups based on similarities.Different from other clustering methods such as neural network and C-means clustering,the FCM substitutes the“soft classification”for the“hard classification”[26].Each sample point belongs to all clusters with a respective membership value in the range of [0,1],instead of merely belonging to single cluster.Thus,a more appropriate classification result can be obtained for the samples in the overlap region.

FCM adopts the iterative method to minimize the value of the objective function,thereby producing an optimal clustering result.The objective function is provided by Eq.(8),as follows:

whereCis the cluster number,μ is the degree of membership,wis the fuzzy constant which controls fuzziness extent between various clusters,giisithn-dimensional sample vector,andmjis the center of clusterj.

Meanwhile,the objective function satisfies the following constraint condition:

The fuzzy membership matrix and cluster center set are updated by Eqs.(10) and (11),respectively,as follows:

FCM includes the following steps.First,the appropriate values for the clustering number,weighting exponent,and termination criterion are selected.Then,the membership matrix and cluster center are initialized.Next,the membership and cluster center are calculated and updated repeatedly until the termination condition is satisfied.In this study,the weighting exponentwis set to 2[27];the maximum number of iteration and the minimum improvement of objective function are 100 and 10-6,respectively.

Additionally,36 experiment data sampled from bubbling,turbulent,and fast flow regimes were obtained to evaluate the FCM method.The flow regimes corresponding to the samples can be clearly identified by the observation method.These chosen samples are far away from the flow regime transition boundaries because observation cannot clearly distinguish flow regimes at these areas.As shown in Fig.2,the identification results are in well agreement with the observation,based on the present method.The above verification confirms the feasibility of the present method in recognizing flow regimes.

Fig.2.The identification results of the FCM method.

4.Results and Discussion

4.1.Flow characteristics

The PSD is able to determine the domain frequency of pressure fluctuations in terms of global definition[28],reflecting the motion frequency of the dominant flow structure.Power spectrum of pressure fluctuations from bubbling,turbulent,fast,and multistage beds is plotted in Fig.3.As can be observed,dominant spectral energy in the bubbling and turbulent bed is distributed in the frequency range of 0–5 Hz.A pronounced peak around 1.1–1.5 Hz is observed in the bubbling flow regime,indicating the frequency of the bubble motion in the bed.Similarly,Qiuet al.[18] obtained the dominant frequency of approximately 1 Hz within the bubbling flow regime by analyzing the volume fraction fluctuations.Jaiboonet al.[29]reported that the dominant frequency of bubble formation was 1.7 Hz.In the turbulent flow regime,the dominant frequency decreases to 0.4–1 Hz,consistent with the study reported by Baiet al.[30].Meanwhile,the energy level of spectrum density decreases.For the fast flow regime,the spectral energy spreads over a wide frequency range but the dominant frequency is very low.This finding implies that the irregularity of pressure fluctuations increases and the periodic gas–solid flow structures decrease.

Fig.3.Power spectrum density of pressure fluctuations in different fluidized beds:(a) and (b) bubbling bed,(c) and (d) turbulent bed,(e) and (f) fast bed,(g) and (h)lower enlarged section of multistage bed,(i) and (j) upper enlarged section of multistage bed.

In the multistage bed,spectrum distributions cover high frequencies and vary with the bed height.In the lower enlarged section,the power spectrum shows two evident peaks at low and high frequencies.The peak with 0.6 Hz dominant frequency is consistent with that in the turbulent flow regime.Different from other tested flow regimes,the peak emerging at high frequency suggests the formation of periodic flow structure in the enlarged section.This finding may be explained by the fact that the turbulent effect generates organized high-frequency motion in the enlarged section.Moreover,the high-frequency peak shifts to high frequency(from 4.2 to 6.4 Hz)with the increased gas velocity and solid circulation flux.In the upper enlarged section,the power-spectrum profiles are similar to that of the fast flow regime,thereby indicating the similarity of flow structures between them.This is possibly because that the gas–solid interaction weakens and solid concentration reduces with the increased bed height,causing relatively low pressure oscillations.

Spectrum analysis shows that the flow patterns in different fluidized beds exhibit distinctions.Single spectrum analysis is restricted to quantify the characteristics of different flow patterns,considering that gas–solid flow system is complex and exhibits multiscale behavior.Similar to the wavelet decompostion that the energy of decomposed subsignal is associated to gas–solid flow structures,the IMFs can also represent different coherent flow structures in the pressure fluctuation signal exhibiting frequency and amplitude modulations.Therefore,the energy distributions of IMFs derived from the HHT are used to characterize the flow patterns.

As shown in Fig.4,in the bubbling bed,the primary energy is occupied by IMFs4–9.This broad distribution indicates that multiple patterns of bubble motions caused by bubbles of various sizes exist [31].With the increased gas velocity,the values of the maximum energy at the scales of IMF5 and IMF6 gradually increase.This is attributed to the fact that bubble motions become intensive and cause large oscillations of the bed[32,33].As turbulent fluidization forms,the highest energy shifts toward fine scales and appears at the scales of IMF3 and IMF4.The reason is that the motions of the bubble or void,resulted from bubble breakup,dominate and generate high-frequency pressure fluctuations [34].In the turbulent flow regime,strong gas–solid mixture increases flow uniformity and produces relatively single flow structure.Therefore,the distribution range of the major energy is narrower than that of the bubbling bed and concentrates at the scales of IMFs3–5.

According to previous studies [31,35],the IMFs can be demarcated into three flow scales in bubbling beds:particle interactions with high frequency and fine IMF scales (microscale),bubbling motions with medium frequency and medium IMF scales (mesoscale),and equipment contributions with low frequency and coarse IMF scales(macroscale).In CFBs,gas becomes a continuous phase and dense-phase solid transforms into dispersed particles and clusters.Correspondingly,the mesoscale flow structure is related to cluster motions [36].As shown in Fig.3(c) and (d),the maximum energy is distributed at the scale of IMF1.In the fast bed and multistage bed,particle-and cluster-gas motions give rise to pressure fluctuations of higher frequency.Consequently,the dominant energy shifts to fine scales.In the fast bed,the energy proportion gradually declines from fine scales to coarse scales.The energy proportions of IMFs3–8 are close to those at the scales of IMFs1–2,suggesting that cluster motion plays an important role in the fast flow regime.However,in the multistage bed,the fluctuation energy has a sharp reduction from IMF1 to IMF3 and then remains at a low level.Furthermore,the maximum energy in the multistage bed is larger than that in the fast bed under identical operating conditions.This finding demonstrates that particle motions become vigorous in the multistage bed.

Fig.4.Typical energy distributions of IMFs of pressure fluctuations from different fluidized beds:(a) bubbling bed,(b) turbulent bed,(c) fast bed,(d) multistage bed.

The variations in energy distribution with operating conditions can be found.At the same solid circulation flux,the energy at the fine scales increases but decreases at the coarse scales with the increase of gas velocity.Conversely,the energy decreases at the fine scales and increases at the coarse scales with the increase of solid circulation flux under the same gas velocity.High solid concentration increases the possibility of cluster formation.Clusters have lower motion frequency than particles;thus,the energy proportion at fine scales decreases [36].

To obtain a better understanding for flow pattern in the multistage fluidized bed,pressure fluctuation characteristics at different scales decomposed by the HHT are analyzed.Power spectrum of pressure signals at fine and coarse scales is illustrated in Fig.5.For component IMF1,the dominant frequency is approximately 10 Hz in the fast bed,indicating the main cycle frequency of the particle behavior.However,two peaks appear due to the increase of flow complexities in the multistage bed.One peak is smaller than 10 Hz and another peak is greater than 10 Hz,implying that single particle motion is transformed into two forms of motion.The low-frequency peak is possibly related to the decrease of gas velocity in the enlarged section.The high dominant frequency of particle motion may be caused by the gas turbulence,which induces intensive gas–solid mixture and enhances the frequency of particle motion.According to Fig.4(d)(Ug=2.0 m?s-1,Gs=0.75-kg?m-2?s-1),the energy at the scale of IMF5 is relatively large for the IMFs reflecting the mesoscale structure.Thus,the IMF5 is used to characterize clusters.The main frequency peak in the fast bed is 3.2 Hz,lower than that of the microscale particle.The periodic frequency of clusters in Fig.5(d) is 5.2 Hz,which is consistent with the result in Fig.3.Large turbulence intensity accelerates the formation and breakup of clusters,thus,the motion frequency increases.

4.2.Flow regime identification

The above analyses confirm the flow characteristics of bubbling,turbulent,and fast flow regimes.The differences and similarities of flow behavior between the multistage bed and other fluidized beds are observed.Thus,whether the flow regime in the multistage bed is a circulating-turbulent flow regime or only one of the three typical flow regimes needs to be further identified.To provide an objective and quantitative result of flow identification,the FCM method is adopted to distinguish the flow regime in the multistage bed.

A key step of implementing the FCM method is to select suitable characteristic parameters.To achieve objective classifications,statistical analyses are commonly used to extract information from signals.Statistical parameters,such as mean,standard deviation,probability density function,and cumulative probability density function,are regarded as the input of the FCM algorithm.Though statistical method is easily conducted,it is hard to extract more available details because of the nonlinear features of pressure fluctuations in fluidized bed.The HHT has been widely used to characterize the hydrodynamics of multiphase systems due to the advantages of processing signals.Thus,the energy fraction of each IMF component calculated from the HHT is selected to represent features of flow regimes.As shown in Fig.5,most of the energy of pressure fluctuations is distributed at the scales of IMFs1–10.Thus,the energy of the first ten IMF components is used as the eigenvectors of clustering analysis.In the experiment,159 groups of experimental data are sampled from bubbling,turbulent,fast,and multistage fluidized beds under a wide range of operating conditions.For a certain flow regime(including at least 25 sets of sampled data),the energy scopes of each IMF component distinguished from other flow patterns are obtained,as listed in Table 1.

Table 1 IMF energy distributions in different fluidized beds.

Fig.5.Power spectrum density of the IMFs of pressure signals at Ug=2.0 m?s-1 and Gs=0.75 kg?m-2?s-1.

Fig.6.Variations in evaluation index with clustering number.

The clustering number in the classification is uncertain due to the unsupervised characterization of FCM.Therefore,the accuracy of clustering results is related to the determination of the optimal clustering number.Generally,to determine the optimal cluster number,the algorithm is run several times with different cluster numbers and then the optimal result is obtained by means of the criterion functions.Various criterion functions have been proposed to evaluate clustering results,and the criterion function defined by Xie and Ben [37] is used in this study.The validity index indicates that the optimal clustering number corresponds to the minimum value within the range ofC=2 toCmax.The flow regime in the lower (E1) and upper (E2) enlarged sections of the multistage bed is identified.If a circulating-turbulent flow regime forms in the multistage bed,then the optimal clustering number is 4;otherwise,the optimal clustering number is 3 and the flow pattern is one of the bubbling (B),turbulent (T),and fast (F) flow regimes.Two data sets,{B,T,F,E1} and {B,T,F,E2},are classified using the FCM algorithm.As plotted in Fig.6,the optimal clustering number is 3,suggesting that circulating-turbulent flow regime does not occur in the multistage bed under examined conditions.

Detailed clustering results are shown in Fig.7.The values on the axis represent the degree of membership.Evidently,all data sampled from the bubbling,turbulent,and fast beds have the largest membership value in the respective flow regime,which is in good agreement with the experimental observations.The results also confirm that the present method provides a good performance in identifying flow regimes.The samples from the multistage bed have the largest membership value in the category of fast flow regime,indicating that the fast flow regime has the highest probability.Therefore,we carefully conclude that the flow regime in the multistage bed is the fast flow regime and not the circulatingturbulent flow regime.Additionally,the identification results of the flow regime in the lower and upper enlarged sections are the same,indicating the consistency of the flow regime in the multistage bed.

Fig.7.Flow regime identification results in multistage bed using FCM for (a) lower enlarged section and (b) upper enlarged section.

Fig.8.Emptying time as a function of gas velocity.

Qiet al.[9]suggested that the circulating-turbulent flow regime exhibits several distinctive features,as follows:(1) high overall solid volume concentration of 0.2–0.35;(2) particle motion dominated by particle–particle interaction compared with gas–particle interaction;(3)no net downflow of solids across the entire column.The level of solid holdup in the multistage bed is smaller than the circulating-turbulent bed due to the operating condition for desulfurization,though solid concentration largely increases in the enlarged section.The improvement of solid concentration and turbulent intensity enhances particle motions (particle collisions and cycle frequency of clusters) in the enlarged section.However,the relatively low solid volume fraction indicates that gas phase occupies primary flow regions and that gas–particle interaction dominates,similar to the fast flow regime.Previous study [5]confirmed that the net downflow of solids near the wall occurred in the enlarged section of multistage bed.Different from the turbulent flow regime characterized by severe solid backmixing,the downward trend of the solid movement is restricted because gas provides sufficient conveying capacity to ensure continuously upward flow of solids in the multistage bed.

In conclusion,the flow behavior in the multistage bed becomes intense and complex due to the changes in bed geometry,thereby resulting in the emergence of some distinctive flow characteristics.On the other hand,superficial gas velocity and solid circulation flux are lower than the case in the dense circulation system,implying that the changes in gas–solid flow behavior,such as turbulence intensity and inter-phase interactions,are finite.Thus,the flow pattern remains low similarities between the multistage bed and the turbulent bed but has a relatively small gap between the multistage bed and the fast bed.

4.3.Flow regime transition

For the dry desulfurization process,the fast fluidization in the bed is required.Superficial gas velocity should be higher than a critical point(i.e.,the onset of turbulent to fast flow regime).However,the flow pattern transition is possibly affected by the bed structure in the multistage bed.To quantitatively describe the transition boundary,the transition velocity from turbulent to fast flow regime is investigated in this section.

The minimum transport velocity represents the boundary between turbulent bed and fast bed.As gas velocity reaches the minimum transport velocity,the transport capacity of gas phase largely increases and the transition from turbulent flow regime to fast flow regime starts.In this study,the emptying-time methodis used to measure the minimum transport velocity due to simplicity and reliability [38].As shown in Fig.8,the emptying time of solids in the bed is measured without the solid recirculation at each specified gas velocity.The minimum transport velocity is defined as the intersection of two lines fitted at low and high gas velocities.Five particles with different densities and diameters are used,as listed in Table 2.

Table 2 Particle properties.

According to the above method,the transport velocities are measured and correlated in the conventional and multistage risers.Fig.9 presents the comparison of transport velocity between the multistage riser (indicated by green line) and the conventional riser(indicated by red line).It can be seen that the transport velocity increases with the increase of Archimedes numberAr,indicating the effects of particle properties on flow regime transition.Turbulent and fast flow regimes successively occur in the conventional riser with increased gas velocity.Compared with the conventional riser,the boundary between turbulent fluidization and fast fluidization moves upwards in the multistage bed.This result indicates that the transport velocity is larger than that in the conventional fast bed for the same particle.Moreover,the gap between them progressively varies depending on solid diameters and densities.The region ranging from red line to green line indicates the variations in flow regime from the conventional equaldiameter riser to the multistage riser.As gas velocity is beyondUtbut less thanUtm,fast flow regime appears in the conventional riser in which solids are continuously entrained out of the column in the form of clusters.Differently,when gas–solid mixing flows into the enlarged section of the multistage bed at the same gas velocity,the carrying capacity of gas reduces because of energy losses.Accordingly,only partial solids obtain adequate energies to flow upwards and leave the enlarged section.The residual solids accumulate and intensively blend with gas in the enlarged section.As gas velocity exceedsUtm,gas remains enough power to carry particles though the interactions between gas and particle are still strong in the enlarged section of multistage bed.

Fig.9.Flow regime transition of activated semi-coke in the multistage and conventional risers.

5.Conclusions

To understand the fluidization mechanism in the novel multistage fluidized bed for desulfurization,flow regime identification and transition were conducted in this work.Pressure signals were sampled from bubbling,turbulent,fast,and multistage fluidized beds.Flow characteristics extracted from pressure signals were analyzed and compared using power spectrum and HHT methods.Flow regime in the multistage bed was identified by the FCM method.The main conclusions are as follows:

(1) Distinctive flow behavior was observed for each flow regime.Multiple patterns of bubble motions indicated by the broad energy distribution occurred in the bubbling bed.The relatively single flow structure with the narrow energy distribution emerged in the turbulent bed.In the multistage bed,gas–particle suspension flow exhibited two dominant motion peaks in low and high frequencies.Moreover,gas–cluster motions became intensive for the multistage bed in comparison with the fast bed.

(2) The FCM method provides a good identification result of flow regime.As a result,the flow pattern in the multistage bed was not a circulating-turbulent flow regime but belonged to the fast flow regime for desulfurization process.Moreover,the flow regime remained consistent in the lower and upper enlarged sections of multistage bed.

(3) The transition velocity of fast fluidization in the multistage bed was higher than that in the conventional bed.Furthermore,the gap between transition boundaries progressively increased with the increase ofAr.

(4) The lowest transport velocity in the multistage CFB should be larger than the flue gas velocity in the conventional CFB for dry desulfurization.On the one hand,gas–solid flow structure is expected to be improved in the multistage bed.On the other hand,the gas velocity needs to be high enough to ensure small pressure drop and flexible operation in the practical process.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

The authors appreciate the financial support from the Taishan Scholar Project of Shandong Province (ts20190937).

Nomenclature

ArArchimedes number

Cclustering number

Cmaxstarting point of monotonically decreasing tendency

dEuler distance

Eisignal energy of each IMF,Pa

fsampling frequency,Hz

Gssolid circulation flux,kg?m-2?s-1

mclustering center

pienergy proportion of each IMF

ReReynolds number

ttime,s

Ugsuperficial gas velocity,m?s-1

Utonset of fast fluidization,m?s-1

Utmonset of fast fluidization in multistage bed,m?s-1

VXBevaluation index

wfuzzy constant

xtime series

θ instantaneous phase

μ membership value

σ standard deviation

ω instantaneous frequency,Hz